Robust optimization approach in travelling salesman problem

Travelling salesman problem is considered one of the greatest mathematical questions of today. It is defined as finding the shortest Hamiltonian path in a graph while visiting all vertices just once. This paper deals with travelling salesman problem while considering some parts of its mathematical model to be uncertain. In simple travelling salesman problem all the route evaluations are known, but in reality it is a common practice that evaluations of routes can be unknown or uncertain. Uncertainty in optimization models can be handled by using stochastic optimization. In this paper we show how to use robust optimization approach towards modelling uncertainty. The robust approach allows an optimization model to remain relatively simple while finding a robust-optimal solution. It also allows to identify deviations of deterministic values. The way of incorporating of robust aspects in the travelling salesman problem is described in detail and shown on an example in the end.